| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2003 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Find range for variable duration |
| Difficulty | Standard +0.3 This is a straightforward critical path analysis question requiring students to identify when activity D becomes critical by setting up and solving simple inequalities. It involves standard D1 techniques (comparing path lengths) with minimal algebraic manipulation, making it slightly easier than average for A-level maths. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
| Activity | Must be preceded by: |
| A | - |
| B | A |
| C | A |
| D | A |
| E | C |
| F | C |
| G | B, \(D , E , F\) |
| H | \(B , D , E , F\) |
| I | F, \(D\) |
| J | G, H, I |
| K | \(F , D\) |
| L | \(K\) |
| Answer | Marks | Guidance |
|---|---|---|
| Precedence network diagram as shown (with nodes A,B,C,D,E,F,G,H,I,J,K,L) | M1, A1, A1, A1, A1, A1 | (6) |
| Answer | Marks | Guidance |
|---|---|---|
| \(ACDEG - 13 + x\) | M1 | |
| So D critical if \(x \geq 2\) (must be \(\geq\) not \(>\)) | A1 | (2) |
# Question 4:
## Part (a)
Precedence network diagram as shown (with nodes A,B,C,D,E,F,G,H,I,J,K,L) | M1, A1, A1, A1, A1, A1 | (6)
## Part (b)
D will only be critical if it lies on a longest route.
$ABEG - 14$
$ACFG - 15$
$ACDEG - 13 + x$ | M1 |
So D critical if $x \geq 2$ (must be $\geq$ not $>$) | A1 | (2)
**Total: 8 marks**
---4. (a) Draw an activity network described in this precedence table, using as few dummies as possible.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Must be preceded by: \\
\hline
A & - \\
\hline
B & A \\
\hline
C & A \\
\hline
D & A \\
\hline
E & C \\
\hline
F & C \\
\hline
G & B, $D , E , F$ \\
\hline
H & $B , D , E , F$ \\
\hline
I & F, $D$ \\
\hline
J & G, H, I \\
\hline
K & $F , D$ \\
\hline
L & $K$ \\
\hline
\end{tabular}
\end{center}
(a) A different project is represented by the activity network shown in Fig. 3. The duration of each activity is shown in brackets.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\includegraphics[alt={},max width=\textwidth]{75ea31c7-11e7-4dd9-9312-4cf32bba622b-05_710_1580_1509_239}
\end{center}
\end{figure}
Find the range of values of $x$ that will make $D$ a critical activity.\\
(2)\\
\hfill \mbox{\textit{Edexcel D1 2003 Q4 [7]}}